Ionic Bonding (6) More on Lattice Energy

Ionic Bonding (6) More on Lattice Energy

Let’s look at some Lattice Energy data and see what we can learn from it.

First, let’s look at how lattice energy changes down a group of the periodic table

Let’s keep the anion the same and change the cation as in this data for the Group 1 chlorides and the Group 2 chlorides:

Group 1 chlorides             Group 2 Chlorides

LiCl                848                BeCl₂              3020

NaCl               780                MgCl₂            2526

KCl                 711                CaCl₂             2258

RbCl               685                SrCl₂              2156

CsCl               661                BaCl₂             2056

Two trends stand out:

First, the Lattice Energy for the chlorides within each group decreases as the cation size, as measured by its ionic radius, increases. 

This decrease occurs, even though the structure of these chlorides changes, as we go down the group e.g. sodium chloride (NaCl) has a face centred cubic lattice with 6:6 coordination.

 Whereas caesium chloride (CsCl) has a body centred cubic lattice structure with 8:8 coordination. 

So despite the structure of the halides changing it is the change in ionic radii of the cations that is significantly affecting the experimentally determined lattice energy. 

The change is likely to give rise to a greater distance between ions. 

Furthermore the charge density of the cation is decreasing and reducing the attractive force between cation and anion.

The polarising effect of the cation on the softer anion is not that significant since the difference between the experimentally determined lattice energy and the corresponding theoretical value is very small.

We also note a second trend that is shown from this data.

The charge on a Group 1 metal ion is 1+ and on Group 2 metal ions 2+ and this accounts for the much larger values for the Group 2 chloride lattice energies. 

Let’s look now at changes to the lattice energy of the halides of Group 1:

Lattice energies of the Sodium Halides (kJ.mol^-1)

NaF                918

NaCl               780

NaBr              742

NaI                 705

Again we observe that the lattice energy falls as we go down the group.

The cation radius remains constant but the anion increases in size.

The anion’s charge density is decreasing as each has the same charge ‘spread’ over a greater surface area. 

The effect is to reduce the force of attraction between ions of opposite charge. 

The other effect that can be seen is that the Iodide has the largest difference between experimental and theoretical lattice energies. 

As predicted the softest lowest charge density ion, in this case Iodide I^-, is the most polarisable by a small highly charge dense cation Na+. 

There is a 28kJmol^-1 difference between the two values for the iodide’s lattice energy.

Here is a typical question from a recent British Advanced level examination paper covering some of the ideas discussed in these blogs on lattice energy (they call lattice energy the lattice enthalpy of dissociation.)

1 (a) Define the term lattice enthalpy of dissociation. ...................................................................................................................................... ....................................................................................................................................... (2 marks) 1 (b) Lattice enthalpy can be calculated theoretically using a perfect ionic model. Explain the meaning of the term perfect ionic model. ...................................................................................................................................... ....................................................................................................................................... 1(c) Suggest two properties of ions that influence the value of a lattice enthalpy calculated using a perfect ionic model. Property 1 .......................................................................................................................... ...................................................................................................................................... Property 2 .......................................................................................................................... .......................................................................................................................................

1 (d)

Use the data in the table below to calculate a value for the lattice enthalpy of dissociation for silver chloride.

Enthalpy of atomisation for silver	+289
First ionisation energy for silver	+732
Enthalpy of atomisation for chlorine	+121
Electron affinity for chlorine	– 364
Enthalpy of formation for silver chloride	–127

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 (3 marks)

1 (e) Predict whether the magnitude of the lattice enthalpy of dissociation that you have calculated in part (d) will be less than, equal to or greater than the value that is obtained from a perfect ionic model. Explain your answer.

Prediction compared with ionic model ...............................................................................

Explanation .

The ionic radius of Ag+ is 0.065nm and of the chloride ion Cl^- 0.180nm.